$\"\"$

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Water is leaking out from the conical tank at a rate of $\"\"$ cm³/min.

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At the same time water is being pumped in to the tank at a constant rate.

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Height of the tank is 6 m and diameter at the top $\"\"$ m.

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Diagram of the situation at any time $\"\"$ :

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$\"\"$

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From the property of the similar triangles.

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$\"\"$

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The volume of the water at any time $\"\"$ is $\"\"$ .

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Substitute $\"\"$ in above formula.

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$\"\"$

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Differentiate on each side with respect to $\"\"$ .

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$\"\"$

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$\"\"$ .

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$ .

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$\"\"$ .

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$\"\"$ .

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Determine the rate at which water is being pumped into the tank when height is $\"\"$ .

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Water level is rising at a rate of $\"\"$ cm/min.

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Substitute $\"\"$ and $\"\"$ in $\"\"$ .

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$\"\"$

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Rate at which water is being pumped into the tank is $\"\"$ cm³/min.

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$\"\"$

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Rate at which water is being pumped in to the tank is $\"\"$ cm³/min.